Answer:
Total distance covered each week is ![11\frac{1}{4}\ miles](https://tex.z-dn.net/?f=11%5Cfrac%7B1%7D%7B4%7D%5C%20miles)
Step-by-step explanation:
Given
Days = 5 days
Distance =
miles
Required
Determine the total distance covered in a week
To do this, we simply multiply distance by number of days.
![Total\ distance = distance * days](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%20distance%20%2A%20days)
![Total\ distance = 2\frac{1}{4} * 5](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%202%5Cfrac%7B1%7D%7B4%7D%20%2A%205)
Convert to improper fraction
![Total\ distance = \frac{9}{4} * 5](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%20%5Cfrac%7B9%7D%7B4%7D%20%2A%205)
![Total\ distance = \frac{9 * 5}{4}](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%20%5Cfrac%7B9%20%2A%205%7D%7B4%7D)
![Total\ distance = \frac{45}{4}](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%20%5Cfrac%7B45%7D%7B4%7D)
![Total\ distance = 11\frac{1}{4}](https://tex.z-dn.net/?f=Total%5C%20distance%20%3D%2011%5Cfrac%7B1%7D%7B4%7D)
Hence, the total distance covered each week is ![11\frac{1}{4}\ miles](https://tex.z-dn.net/?f=11%5Cfrac%7B1%7D%7B4%7D%5C%20miles)
Answer:
3(x-3)(x+3)
Step-by-step explanation:
First, factor out 3 from the expression: 3(x²-9)
Second, use a²-b²=(a-b)(a+b) to factor the expression: 3(x-3) · (x+3)
Answer:
I think it would be D, but can you correct me if I'm wrong :)
Step-by-step explanation:
If it's + 3, it will move over to the right 3 times
Hope that this helps you and have a great day :)
Answer and explanation:
Given : At Tech Express, 40% of the customers purchases small coffee and 60% purchases medium. Of those customers purchasing small coffee, 30% prefer decaf. Of those purchasing medium coffee, 50% prefer decaf.
Let
customer purchase small coffee.
i.e. ![P(A_1)=40\%=0.4](https://tex.z-dn.net/?f=P%28A_1%29%3D40%5C%25%3D0.4)
customer purchase medium coffee.
i.e. ![P(A_2)=60\%=0.6](https://tex.z-dn.net/?f=P%28A_2%29%3D60%5C%25%3D0.6)
Let B be the customer purchase prefer decaf.
So, ![P(B|A_1)=30\%=0.3](https://tex.z-dn.net/?f=P%28B%7CA_1%29%3D30%5C%25%3D0.3)
![P(B|A_2)=50\%=0.5](https://tex.z-dn.net/?f=P%28B%7CA_2%29%3D50%5C%25%3D0.5)
(a) What is the probability that the next customer will request medium and decaf coffee?
i.e. ![P(A_2\cap B)=P(A_2)\times P(B|A_2)](https://tex.z-dn.net/?f=P%28A_2%5Ccap%20B%29%3DP%28A_2%29%5Ctimes%20P%28B%7CA_2%29)
![P(A_2\cap B)=0.6\times 0.5](https://tex.z-dn.net/?f=P%28A_2%5Ccap%20B%29%3D0.6%5Ctimes%200.5)
![P(A_2\cap B)=0.3](https://tex.z-dn.net/?f=P%28A_2%5Ccap%20B%29%3D0.3)
(b) What is the probability that the next customer prefers decaf?
i.e. ![P(B)=P(A_1\cap B)+P(A_2\cap B)](https://tex.z-dn.net/?f=P%28B%29%3DP%28A_1%5Ccap%20B%29%2BP%28A_2%5Ccap%20B%29)
![P(B)=P(A_1)\times P(B|A_1)+P(A_2)\times P(B|A_2)](https://tex.z-dn.net/?f=P%28B%29%3DP%28A_1%29%5Ctimes%20P%28B%7CA_1%29%2BP%28A_2%29%5Ctimes%20P%28B%7CA_2%29)
![P(B)=0.4\times 0.3+0.6\times 0.5](https://tex.z-dn.net/?f=P%28B%29%3D0.4%5Ctimes%200.3%2B0.6%5Ctimes%200.5)
![P(B)=0.12+0.3](https://tex.z-dn.net/?f=P%28B%29%3D0.12%2B0.3)
![P(B)=0.42](https://tex.z-dn.net/?f=P%28B%29%3D0.42)
(c) If the next customer prefers decaf, what is the probability that small is requested?
i.e. ![P(A_1|B)=\frac{P(A_1\cap B)}{P(B)}](https://tex.z-dn.net/?f=P%28A_1%7CB%29%3D%5Cfrac%7BP%28A_1%5Ccap%20B%29%7D%7BP%28B%29%7D)
![P(A_1|B)=\frac{0.12}{0.42}](https://tex.z-dn.net/?f=P%28A_1%7CB%29%3D%5Cfrac%7B0.12%7D%7B0.42%7D)
![P(A_1|B)=0.28](https://tex.z-dn.net/?f=P%28A_1%7CB%29%3D0.28)
Answer:
Distribute the 6 to the terms inside the parentheses.
5=6q-30-19
Combine like terms.
5=6q-49
Add 49 to both sides.
54=6q
Divide both sides by 6.
q=9
:)